President Barack Obama made good on the promise of his second inaugural address Thursday by joining the fight to overturn California’s ban on same-sex marriage. Having declared that marriage equality is part of the road “through Seneca Falls and Selma and Stonewall,” we can’t imagine how he could have sat this one out.

The administration’s brief to the Supreme Court was a legally and symbolically important repudiation of Proposition 8, the 2008 voter referendum that amended California’s constitution to forbid bestowing the title of marriage on a union between two people of the same sex — a right the California Supreme Court had found to be fundamental under the state constitution.

Like the arguments made by the lawyers for those who seek to overturn Proposition 8, and by a group of prominent Republicans earlier this week, the government’s brief says any law attempting to ban same-sex marriage must be subjected to heightened scrutiny because it singles out a class of Americans, historically subject to discrimination, for unequal treatment.

The brief said California’s civil unions law provides the rights and protections of marriage, so Proposition 8’s denial of the designation of marriage “does not substantially further any important governmental interest.”

The government made mincemeat of the argument that same-sex couples threaten “traditional” marriage. “Petitioners’ central argument is that Proposition 8 advances an interest in responsible procreation and child-rearing because only heterosexual couples can produce ‘unintended pregnancies’ and because the ‘overriding purpose’ of marriage is to address that reality by affording a stable institution for procreation and child-rearing,” the brief said. “But, as this court has recognized, marriage is far more than a societal means of dealing with unintended pregnancies.”

Proposition 8, it said, neither promotes opposite-sex parenting nor prevents same-sex parenting. In any case, “the overwhelming expert consensus is that children raised by gay and lesbian parents are as likely to be well adjusted as children raised by heterosexual parents.”

The legal analysis advanced by the Obama administration leads inexorably to the conclusion that all attempts to ban same-sex marriage are inherently unconstitutional. But the administration stopped short of declaring that truth, recognized earlier this week even by the Republicans’ brief. In fact, the administration said the court need not consider the constitutionality of marriage bans beyond the context of this particular scheme.

We don’t know why the administration did not take that step. Perhaps it was to allow Obama to go on asserting that the issue of same-sex marriage should generally be left up to the states. We hope the justices recognize the broader truth that the Constitution does not tolerate denying gay people the right to wed in any state.